What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
8001 | 2^346750+140967 | 104383 | Stefano Morozzi | 11/2024 |
8002 | 2^346751+48515 | 104383 | Stefano Morozzi | 11/2024 |
8003 | 2^346751+74481 | 104383 | Stefano Morozzi | 11/2024 |
8004 | 2^346752+103497 | 104383 | Stefano Morozzi | 11/2024 |
8005 | 2^346747+4589 | 104382 | Stefano Morozzi | 11/2024 |
8006 | 2^346747+29969 | 104382 | Stefano Morozzi | 11/2024 |
8007 | 2^346747+130973 | 104382 | Stefano Morozzi | 11/2024 |
8008 | 2^346748+184387 | 104382 | Stefano Morozzi | 11/2024 |
8009 | 2^346743+39545 | 104381 | Stefano Morozzi | 11/2024 |
8010 | 2^346743+61335 | 104381 | Stefano Morozzi | 11/2024 |
8011 | 2^346746+99025 | 104381 | Stefano Morozzi | 11/2024 |
8012 | 2^346737+39431 | 104379 | Stefano Morozzi | 11/2024 |
8013 | 2^346733+96437 | 104378 | Stefano Morozzi | 11/2024 |
8014 | 2^346736+83025 | 104378 | Stefano Morozzi | 11/2024 |
8015 | 2^346736+196405 | 104378 | Stefano Morozzi | 11/2024 |
8016 | 2^346732+72685 | 104377 | Stefano Morozzi | 11/2024 |
8017 | 2^346727+86903 | 104376 | Stefano Morozzi | 11/2024 |
8018 | 2^346727+89829 | 104376 | Stefano Morozzi | 11/2024 |
8019 | 2^346729+199319 | 104376 | Stefano Morozzi | 11/2024 |
8020 | 2^346723+73521 | 104375 | Stefano Morozzi | 11/2024 |
8021 | 2^346724+91177 | 104375 | Stefano Morozzi | 11/2024 |
8022 | 2^346726+191527 | 104375 | Stefano Morozzi | 11/2024 |
8023 | 2^346720+235 | 104374 | Stefano Morozzi | 11/2024 |
8024 | 2^346720+189435 | 104374 | Stefano Morozzi | 11/2024 |
8025 | 2^346718+124833 | 104373 | Stefano Morozzi | 11/2024 |
8026 | 2^346718+127029 | 104373 | Stefano Morozzi | 11/2024 |
8027 | 2^346719+129291 | 104373 | Stefano Morozzi | 11/2024 |
8028 | 2^346719+183033 | 104373 | Stefano Morozzi | 11/2024 |
8029 | 2^346714+81909 | 104372 | Stefano Morozzi | 11/2024 |
8030 | 2^346714+174493 | 104372 | Stefano Morozzi | 11/2024 |
8031 | 2^346716+174123 | 104372 | Stefano Morozzi | 11/2024 |
8032 | 2^346711+160659 | 104371 | Stefano Morozzi | 11/2024 |
8033 | 2^346710+143649 | 104371 | Stefano Morozzi | 11/2024 |
8034 | 2^346712+52063 | 104371 | Stefano Morozzi | 11/2024 |
8035 | 2^346707+27099 | 104370 | Stefano Morozzi | 11/2024 |
8036 | 2^346708+26217 | 104370 | Stefano Morozzi | 11/2024 |
8037 | 2^346708+165715 | 104370 | Stefano Morozzi | 11/2024 |
8038 | 2^346705+6581 | 104369 | Stefano Morozzi | 11/2024 |
8039 | 2^346705+39851 | 104369 | Stefano Morozzi | 11/2024 |
8040 | 2^346706+172963 | 104369 | Stefano Morozzi | 11/2024 |
8043 | 3^218744+58 | 104368 | Lelio R Paula | 11/2016 |
8041 | 2^346700+191515 | 104368 | Stefano Morozzi | 11/2024 |
8042 | 2^346701+164841 | 104368 | Stefano Morozzi | 11/2024 |
8044 | 2^346694+20437 | 104366 | Stefano Morozzi | 11/2024 |
8045 | 2^346694+131557 | 104366 | Stefano Morozzi | 11/2024 |
8046 | 2^346695+6795 | 104366 | Stefano Morozzi | 11/2024 |
8047 | 2^346691+158613 | 104365 | Stefano Morozzi | 11/2024 |
8048 | 2^346692+122623 | 104365 | Stefano Morozzi | 11/2024 |
8049 | 2^346687+188033 | 104364 | Stefano Morozzi | 11/2024 |
8050 | 2^346688+71005 | 104364 | Stefano Morozzi | 11/2024 |
8051 | 2^346688+89811 | 104364 | Stefano Morozzi | 11/2024 |
8052 | 2^346688+122115 | 104364 | Stefano Morozzi | 11/2024 |
8053 | 2^346689+100829 | 104364 | Stefano Morozzi | 11/2024 |
8054 | 2^346689+172847 | 104364 | Stefano Morozzi | 11/2024 |
8055 | 2^346685+136145 | 104363 | Stefano Morozzi | 11/2024 |
8058 | 9*10^104361+89 | 104362 | Robert Price | 11/2019 |
8056 | 2^346681+58601 | 104362 | Stefano Morozzi | 11/2024 |
8057 | 2^346681+186111 | 104362 | Stefano Morozzi | 11/2024 |
8059 | 2^346676+82285 | 104360 | Stefano Morozzi | 11/2024 |
8060 | 2^346670+69985 | 104359 | Stefano Morozzi | 11/2024 |
8061 | 2^346672+85371 | 104359 | Stefano Morozzi | 11/2024 |
8062 | 2^346673+47231 | 104359 | Stefano Morozzi | 11/2024 |
8068 | 25048^14665+14665^25048 | 104358 | Hans Havermann | 09/2020 |
8063 | 2^346667+84359 | 104358 | Stefano Morozzi | 11/2024 |
8064 | 2^346668+26391 | 104358 | Stefano Morozzi | 11/2024 |
8065 | 2^346668+138987 | 104358 | Stefano Morozzi | 11/2024 |
8066 | 2^346669+27735 | 104358 | Stefano Morozzi | 11/2024 |
8067 | 2^346669+33989 | 104358 | Stefano Morozzi | 11/2024 |
8069 | 2^346664+16377 | 104357 | Stefano Morozzi | 11/2024 |
8070 | 2^346666+29595 | 104357 | Stefano Morozzi | 11/2024 |
8071 | 2^346660+61095 | 104356 | Stefano Morozzi | 11/2024 |
8072 | 2^346661+114311 | 104356 | Stefano Morozzi | 11/2024 |
8073 | 2^346662+75745 | 104356 | Stefano Morozzi | 11/2024 |
8074 | 2^346663+123305 | 104356 | Stefano Morozzi | 11/2024 |
8075 | 2^346662+150475 | 104356 | Stefano Morozzi | 11/2024 |
8076 | 2^346658+28393 | 104355 | Stefano Morozzi | 11/2024 |
8077 | 2^346658+137619 | 104355 | Stefano Morozzi | 11/2024 |
8078 | 2^346659+86415 | 104355 | Stefano Morozzi | 11/2024 |
8079 | 2^346659+117849 | 104355 | Stefano Morozzi | 11/2024 |
8080 | 2^346655+199859 | 104354 | Stefano Morozzi | 11/2024 |
8081 | 2^346656+100627 | 104354 | Stefano Morozzi | 11/2024 |
8082 | 2^346651+88491 | 104353 | Stefano Morozzi | 11/2024 |
8083 | 2^346652+32971 | 104353 | Stefano Morozzi | 11/2024 |
8084 | 2^346652+85321 | 104353 | Stefano Morozzi | 11/2024 |
8085 | 2^346652+100627 | 104353 | Stefano Morozzi | 11/2024 |
8086 | 2^346652+190255 | 104353 | Stefano Morozzi | 11/2024 |
8087 | 2^346652+194667 | 104353 | Stefano Morozzi | 11/2024 |
8088 | 2^346652+197073 | 104353 | Stefano Morozzi | 11/2024 |
8092 | 2^346649+65 | 104352 | Lelio R Paula | 09/2011 |
8089 | 2^346647+128475 | 104352 | Stefano Morozzi | 11/2024 |
8090 | 2^346647+181169 | 104352 | Stefano Morozzi | 11/2024 |
8091 | 2^346648+97381 | 104352 | Stefano Morozzi | 11/2024 |
8093 | (19*33^68718-600883)/32 | 104350 | Eric Chen | 05/2023 |
8094 | 2^346640+73723 | 104350 | Stefano Morozzi | 11/2024 |
8095 | 2^346641+169667 | 104350 | Stefano Morozzi | 11/2024 |
8096 | 2^346642+100395 | 104350 | Stefano Morozzi | 11/2024 |
8097 | 2^346643+61025 | 104350 | Stefano Morozzi | 11/2024 |
8098 | 2^346643+160785 | 104350 | Stefano Morozzi | 11/2024 |
8100 | 2^346638-17265 | 104349 | Enzo Doria | 05/2013 |
8099 | 2^346637+34139 | 104349 | Stefano Morozzi | 11/2024 |
8101 | 2^346635+13071 | 104348 | Stefano Morozzi | 11/2024 |
8102 | 2^346630+66003 | 104347 | Stefano Morozzi | 11/2024 |
8103 | 2^346630+187137 | 104347 | Stefano Morozzi | 11/2024 |
8104 | 2^346631+27393 | 104347 | Stefano Morozzi | 11/2024 |
8105 | 2^346632+21883 | 104347 | Stefano Morozzi | 11/2024 |
8106 | 2^346632+136015 | 104347 | Stefano Morozzi | 11/2024 |
8107 | 2^346628+87907 | 104346 | Stefano Morozzi | 11/2024 |
8108 | 2^346624+174075 | 104345 | Stefano Morozzi | 11/2024 |
8109 | 2^346620+87451 | 104344 | Stefano Morozzi | 11/2024 |
8110 | 2^346622+12247 | 104344 | Stefano Morozzi | 11/2024 |
8111 | 2^346623+69161 | 104344 | Stefano Morozzi | 11/2024 |
8112 | 2^346614+85737 | 104342 | Stefano Morozzi | 11/2024 |
8113 | 2^346611+183923 | 104341 | Stefano Morozzi | 11/2024 |
8114 | 2^346607+36209 | 104340 | Stefano Morozzi | 11/2024 |
8115 | 2^346607+65291 | 104340 | Stefano Morozzi | 11/2024 |
8116 | 2^346609+47471 | 104340 | Stefano Morozzi | 11/2024 |
8121 | (2^346606+2082)/2 | 104339 | Stefano Morozzi | 09/2020 |
8122 | (2^346607+2070)/2 | 104339 | Stefano Morozzi | 09/2020 |
8117 | 2^346605+1041 | 104339 | Stefano Morozzi | 11/2024 |
8118 | 2^346605+181167 | 104339 | Stefano Morozzi | 11/2024 |
8119 | 2^346606+1035 | 104339 | Stefano Morozzi | 11/2024 |
8120 | 2^346606+103863 | 104339 | Stefano Morozzi | 11/2024 |
8123 | 2^346601+26529 | 104338 | Stefano Morozzi | 11/2024 |
8124 | 2^346603+133431 | 104338 | Stefano Morozzi | 11/2024 |
8125 | 2^346597+97661 | 104337 | Stefano Morozzi | 11/2024 |
8126 | 2^346597+186809 | 104337 | Stefano Morozzi | 11/2024 |
8127 | 2^346598+31719 | 104337 | Stefano Morozzi | 11/2024 |
8128 | 2^346598+162513 | 104337 | Stefano Morozzi | 11/2024 |
8129 | 2^346599+45731 | 104337 | Stefano Morozzi | 11/2024 |
8130 | 2^346599+187061 | 104337 | Stefano Morozzi | 11/2024 |
8131 | 2^346600+175993 | 104337 | Stefano Morozzi | 11/2024 |
8132 | 2^346595+89753 | 104336 | Stefano Morozzi | 11/2024 |
8133 | 2^346595+114491 | 104336 | Stefano Morozzi | 11/2024 |
8134 | 2^346596+120183 | 104336 | Stefano Morozzi | 11/2024 |
8135 | 2^346591+183651 | 104335 | Stefano Morozzi | 11/2024 |
8136 | 2^346591+192149 | 104335 | Stefano Morozzi | 11/2024 |
8137 | 2^346592+77347 | 104335 | Stefano Morozzi | 11/2024 |
8138 | 2^346592+178161 | 104335 | Stefano Morozzi | 11/2024 |
8139 | 2^346592+195985 | 104335 | Stefano Morozzi | 11/2024 |
8140 | 2^346589+40607 | 104334 | Stefano Morozzi | 11/2024 |
8141 | 2^346590+151533 | 104334 | Stefano Morozzi | 11/2024 |
8142 | 2^346584+105103 | 104333 | Stefano Morozzi | 11/2024 |
8143 | 2^346585+56861 | 104333 | Stefano Morozzi | 11/2024 |
8149 | (2^346582+3202)/2 | 104332 | Stefano Morozzi | 09/2020 |
8144 | 2^346581+1601 | 104332 | Stefano Morozzi | 11/2024 |
8145 | 2^346581+82115 | 104332 | Stefano Morozzi | 11/2024 |
8146 | 2^346581+193979 | 104332 | Stefano Morozzi | 11/2024 |
8147 | 2^346582+197767 | 104332 | Stefano Morozzi | 11/2024 |
8148 | 2^346583+116579 | 104332 | Stefano Morozzi | 11/2024 |
8150 | 26092^9967+9967^26092 | 104331 | Hans Havermann | 09/2020 |
8151 | 2^346577+47501 | 104331 | Stefano Morozzi | 11/2024 |
8152 | 2^346578+163287 | 104331 | Stefano Morozzi | 11/2024 |
8153 | 2^346579+37019 | 104331 | Stefano Morozzi | 11/2024 |
8154 | 2^346579+119645 | 104331 | Stefano Morozzi | 11/2024 |
8155 | 2^346579+157611 | 104331 | Stefano Morozzi | 11/2024 |
8156 | 2^346576+100803 | 104330 | Stefano Morozzi | 11/2024 |
8157 | 2^346576+144495 | 104330 | Stefano Morozzi | 11/2024 |
8158 | 2^346573+13859 | 104329 | Stefano Morozzi | 11/2024 |
8159 | 2^346568+110181 | 104328 | Stefano Morozzi | 11/2024 |
8161 | 5*10^104326+77 | 104327 | Robert Price | 12/2018 |
8160 | 2^346564+151101 | 104327 | Stefano Morozzi | 11/2024 |
8167 | (2^346564+2026)/2 | 104326 | Stefano Morozzi | 09/2020 |
8162 | 2^346561+53385 | 104326 | Stefano Morozzi | 11/2024 |
8163 | 2^346561+139791 | 104326 | Stefano Morozzi | 11/2024 |
8164 | 2^346562+110383 | 104326 | Stefano Morozzi | 11/2024 |
8165 | 2^346563+1013 | 104326 | Stefano Morozzi | 11/2024 |
8166 | 2^346563+9305 | 104326 | Stefano Morozzi | 11/2024 |
8168 | 2^346558+97033 | 104325 | Stefano Morozzi | 11/2024 |
8169 | 2^346556+101283 | 104324 | Stefano Morozzi | 11/2024 |
8170 | 2^346551+55043 | 104323 | Stefano Morozzi | 11/2024 |
8171 | 2^346547+71855 | 104322 | Stefano Morozzi | 11/2024 |
8172 | 2^346548+119695 | 104322 | Stefano Morozzi | 11/2024 |
8173 | 2^346550+55249 | 104322 | Stefano Morozzi | 11/2024 |
8174 | 2^346550+158655 | 104322 | Stefano Morozzi | 11/2024 |
8175 | 2^346545+87885 | 104321 | Stefano Morozzi | 11/2024 |
8176 | 2^346545+95105 | 104321 | Stefano Morozzi | 11/2024 |
8177 | 2^346546+126763 | 104321 | Stefano Morozzi | 11/2024 |
8178 | 2^346546+149397 | 104321 | Stefano Morozzi | 11/2024 |
8179 | (8925^26569-1)/(8925^163-1) | 104320 | Ryan Propper | 11/2023 |
8180 | 2^346542+128005 | 104320 | Stefano Morozzi | 11/2024 |
8181 | 2^346538+123507 | 104319 | Stefano Morozzi | 11/2024 |
8182 | 2^346540+118251 | 104319 | Stefano Morozzi | 11/2024 |
8183 | 2^346540+128965 | 104319 | Stefano Morozzi | 11/2024 |
8184 | 2^346535+138485 | 104318 | Stefano Morozzi | 11/2024 |
8185 | 2^346536+149013 | 104318 | Stefano Morozzi | 11/2024 |
8186 | 2^346531+98801 | 104317 | Stefano Morozzi | 11/2024 |
8187 | 2^346533+12035 | 104317 | Stefano Morozzi | 11/2024 |
8191 | 2^346527-111817 | 104316 | Enzo Doria | 05/2014 |
8190 | 6^134055+101 | 104316 | Lelio R Paula | 11/2016 |
8188 | fibonacci(499147)-4 | 104316 | Jon Grantham | 08/2023 |
8189 | 2^346529+101351 | 104316 | Stefano Morozzi | 11/2024 |
8192 | 2^346524+81585 | 104315 | Stefano Morozzi | 11/2024 |
8193 | 2^346524+184821 | 104315 | Stefano Morozzi | 11/2024 |
8194 | 2^346525+41051 | 104315 | Stefano Morozzi | 11/2024 |
8195 | 2^346525+61845 | 104315 | Stefano Morozzi | 11/2024 |
8196 | 2^346521+47439 | 104314 | Stefano Morozzi | 11/2024 |
8197 | 2^346522+34689 | 104314 | Stefano Morozzi | 11/2024 |
8198 | 2^346519+24543 | 104313 | Stefano Morozzi | 11/2024 |
8199 | 2^346519+75119 | 104313 | Stefano Morozzi | 11/2024 |
8203 | 92105!4+8 | 104312 | Robert Price | 09/2019 |
8200 | 2^346514+11023 | 104312 | Stefano Morozzi | 11/2024 |
8201 | 2^346514+22009 | 104312 | Stefano Morozzi | 11/2024 |
8202 | 2^346516+107031 | 104312 | Stefano Morozzi | 11/2024 |
8204 | 2^346511+65675 | 104311 | Stefano Morozzi | 11/2024 |
8205 | 2^346512+105345 | 104311 | Stefano Morozzi | 11/2024 |
8206 | 2^346513+80387 | 104311 | Stefano Morozzi | 11/2024 |
8207 | 2^346510+104955 | 104310 | Stefano Morozzi | 11/2024 |
8208 | 2^346510+145347 | 104310 | Stefano Morozzi | 11/2024 |
8209 | 2^346506+105537 | 104309 | Stefano Morozzi | 11/2024 |
8210 | 2^346506+145353 | 104309 | Stefano Morozzi | 11/2024 |
8211 | 2^346503+160109 | 104308 | Stefano Morozzi | 11/2024 |
8212 | 2^346494+155215 | 104306 | Stefano Morozzi | 11/2024 |
8213 | 2^346495+26243 | 104306 | Stefano Morozzi | 11/2024 |
8214 | 2^346497+108749 | 104306 | Stefano Morozzi | 11/2024 |
8215 | 2^346488+146631 | 104304 | Stefano Morozzi | 11/2024 |
8216 | 2^346489+6035 | 104304 | Stefano Morozzi | 11/2024 |
8217 | 2^346489+16389 | 104304 | Stefano Morozzi | 11/2024 |
8218 | 2^346489+175959 | 104304 | Stefano Morozzi | 11/2024 |
8219 | 2^346484+119491 | 104303 | Stefano Morozzi | 11/2024 |
8220 | 2^346487+12125 | 104303 | Stefano Morozzi | 11/2024 |
8221 | 2^346487+92103 | 104303 | Stefano Morozzi | 11/2024 |
8222 | 2^346481+199815 | 104302 | Stefano Morozzi | 11/2024 |
8223 | 2^346478+2335 | 104301 | Stefano Morozzi | 11/2024 |
8224 | 2^346478+121773 | 104301 | Stefano Morozzi | 11/2024 |
8225 | 2^346479+80703 | 104301 | Stefano Morozzi | 11/2024 |
8226 | 2^346479+164693 | 104301 | Stefano Morozzi | 11/2024 |
8227 | 2^346480+156951 | 104301 | Stefano Morozzi | 11/2024 |
8228 | 2^346480+176247 | 104301 | Stefano Morozzi | 11/2024 |
8229 | 2^346475+178953 | 104300 | Stefano Morozzi | 11/2024 |
8230 | 2^346476+83935 | 104300 | Stefano Morozzi | 11/2024 |
8231 | 2^346470+182623 | 104298 | Stefano Morozzi | 11/2024 |
8232 | 2^346464+54007 | 104297 | Stefano Morozzi | 11/2024 |
8233 | 2^346464+55287 | 104297 | Stefano Morozzi | 11/2024 |
8234 | 2^346464+84411 | 104297 | Stefano Morozzi | 11/2024 |
8235 | 2^346465+15905 | 104297 | Stefano Morozzi | 11/2024 |
8236 | 2^346465+27797 | 104297 | Stefano Morozzi | 11/2024 |
8237 | 2^346465+85815 | 104297 | Stefano Morozzi | 11/2024 |
8238 | 2^346465+92787 | 104297 | Stefano Morozzi | 11/2024 |
8239 | 2^346466+133369 | 104297 | Stefano Morozzi | 11/2024 |
8240 | 2^346461+30591 | 104296 | Stefano Morozzi | 11/2024 |
8241 | 2^346462+74067 | 104296 | Stefano Morozzi | 11/2024 |
8242 | 2^346458+68947 | 104295 | Stefano Morozzi | 11/2024 |
8243 | 2^346459+39333 | 104295 | Stefano Morozzi | 11/2024 |
8244 | 2^346459+110355 | 104295 | Stefano Morozzi | 11/2024 |
8245 | 2^346454+166035 | 104294 | Stefano Morozzi | 11/2024 |
8246 | 2^346456+132385 | 104294 | Stefano Morozzi | 11/2024 |
8247 | 2^346456+138727 | 104294 | Stefano Morozzi | 11/2024 |
8248 | 2^346456+176767 | 104294 | Stefano Morozzi | 11/2024 |
8249 | 2^346451+72969 | 104293 | Stefano Morozzi | 11/2024 |
8250 | 2^346452+10441 | 104293 | Stefano Morozzi | 11/2024 |